An experiment-design methodology for the selection of optimal experimental conditions for the correlation of transport properties

In accordance with the pioneering work of Rosenfeld, our recent research activities on transport properties (viscosities, thermal conductivities, self-diffusion coefficients) lead to the conclusion that there is a univariate dependence of reduced transport properties on residual entropy where the reduced transport property is a dimensionless ratio of the transport property and a suitable reference quantity. This is the basis of the proposed entropy scaling method in which an equation of state is used not only to estimate the residual entropy of any fluid at specified temperature and pressure but also the reference quantity. The link between the residual entropy and the reduced transport property can be made through a correlation involving six component-dependent param-eters that need to be fitted to experimental data to accurately correlate any given transport property throughout the whole fluid region (liquid, gas and supercritical states). Starting from this observation, the present study proposes to identify the minimum number of experimental measurements, and the corresponding temperature and pressure conditions, to fully characterize a given transport property of a specified compound through a design of experiments-like approach. In this note, it is shown that six experimental data points are sufficient to determine the six parameters of the entropy-scaling based correlation for a given property, provided that the temperatures and pressures of these six data points are properly chosen. A methodology to select the optimal temperature and pressure conditions for these six data is proposed here. Eventually, to characterize the transport property behavior of a given species, experimentalists are advised to perform measurements of the transport properties for all six sets of temperatures and pressures and then, to use our general correlation with parameters fitted to these six experimental data to estimate the transport property in other temperature and pressure conditions.